Answer:
none
Step-by-step explanation:
you ttttttttttttttttttttttttthhhhhhhhhhhhhhhhhhhhhoooooooooooooooooooouuuuuuuuuuuuuuuggggggggggggggggggggghhhhhhhhhhhhhhhhhhhhhhhhtttttttttttt
Answer:
94.76°
Step-by-step explanation:
Assuming the coordinates are <E, N>, the total distance from the start is ...
5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>
These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...
arctan(24/2) = 85.24°
The bearing is 180° -85.24° = 94.76°.
Answer:
y=-3/2x+6
Step-by-step explanation:
Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
1) we calculate the volume of the first carton:
volume=length x width x height
volume=3 ft * 2 ft * 2 ft=12 ft³
Therefore:
A machine can fill 12 ft³ in 3 seconds.
2) we calculate the volume of the second carton.
volume=length x width x heigth
volume=4 ft * 5 ft * 6 ft=120 ft³
3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.
12 ft³---------------------3 seconds
120 ft³-------------------- x
x=(120 ft³ * 3 seconds) / 12 ft³=30 seconds.
answer: 30 seconds.
